In this game, the only dominant strategy is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Gabriel chooses and Nia chooses
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- 7. Solving for dominant strategies and the Nash equilibrium Suppose Russell and Aaliyah are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Russell chooses Up and Aaliyah chooses Down, Russell will receive a payoff of 6 and Aaliyah will receive a payoff of 4. Russell Up Down Aaliyah Up 6,3 3,3 Down 6,4 7,4 In this game, the only dominant strategy is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Russell chooses and Aaliyah chooses7. Solving for dominant strategies and the Nash equilibrium Suppose Rajiv and Simone are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Rajiv chooses Right and Simone chooses Right, Rajiv will receive a payoff of 5 and Simone will receive a payoff of 5.7. Solving for dominant strategies and the Nash equilibrium Suppose Antonio and Caroline are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Antonio chooses Right and Caroline chooses Right, Antonio will receive a payoff of 9 and Caroline will receive a payoff of 8. Caroline Left Right Left 8, 5 8. 7 Antonio Right 3, 6 9, 8 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Antonio chooses and Caroline chooses
- 7. Solving for dominant strategies and the Nash equilibrium Suppose Van and Amy are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Van chooses Right and Amy chooses Right, Van will receive a payoff of 5 and Amy will receive a payoff of 4. Van Left Left 8,3 Right 5,3 Amy Right 4,4 5,4 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Van chooses and Amy chooses5. Consider a simultaneous game in which player A chooses one of two actions (Up or Down), and B chooses one of two actions (Left or Right). The game has the following payoff matrix, where the first payoff in each entry is for A and the second for B.(8 points) B Right Left 3,3 5,1 Down 2,2 4,4 a. Find the Nash equilibrium or equilibria. b. Which player, if any, has a dominant strategy? A Up7. Solving for dominant strategies and the Nash equilibrium Suppose Rashard and Alyssa are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Rashard chooses Up and Alyssa chooses Down, Rashard will receive a payoff of 6 and Alyssa will receive a payoff of 8. Rashard Up Down Alyssa Up 4,6 7,5 Down 6,8 3,7 In this game, the only dominant strategy is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Rashard chooses and Alyssa chooses
- 8. Solving for dominant strategies and the Nash equilibrium Suppose Tim and Alyssa are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Tim chooses Right and Alyssa chooses Right, Tim will receive a payoff of 3 and Alyssa will receive a payoff of 6. Tim Left Left 5, 6 Right 4, 2 Alyssa Right 5,5 3,6 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Tim chooses and Alyssa chooses7. Solving for dominant strategies and the Nash equilibrium Suppose Carlos and Deborah are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Carlos chooses Right and Deborah chooses Right, Carlos will receive a payoff of 5 and Deborah will receive a payoff of 1. Carlos Deborah Left Left 4,4 Right 2,4 Right 6,7 5,1 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Carlos chooses and Deborah chooses7. Solving for dominant strategies and the Nash equilibrium Suppose Dmitri and Frances are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Dmitri chooses Right and Frances chooses Right, Dmitri will receive a payoff of 7 and Frances will receive a payoff of 6. Frances Left Right Left 4, 3 6, 4 Dmitri Right 6, 7 7, 6 to choose The only dominant strategy in this game is for and Frances chooses The outcome reflecting the unique Nash equilibrium in this game is as follows: Dmitri chooses v
- 3. Solving for dominant strategies and the Nash equilibrium Suppose Charles and Dina are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Charles chooses Right and Dina chooses Right, Charles will receive a payoff of 3 and Dina will receive a payoff of 8. Dina Left Right Left 3,7 2,6 Charles Right 4,5 3,8 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Charles chooses and Dina chooses7. Solving for dominant strategies and the Nash equilibrium Suppose Andrew and Beth are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Andrew chooses Right and Beth chooses Right, Andrew will receive a payoff of 6 and Beth will receive a payoff of 5. Andrew Left Right Left 8,4 5,4 Beth Right 4,5 6,5 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Andrew chooses and Beth choosesConsider the payoff matrix for a game depicted below. Player 1 selects the row and Player 2 selects the column. Up Down Left 1, -1 -1, 1 Right -1, 1 1, -1 What is (are) the Nash equilibrium (equilibria)? Question 18Answer a. Player 1 plays right; Player 2 plays down b. Player 1 plays left; Player 2 plays down c. Player 1 plays down; Player 2 plays left d. Player 1 plays right; Player 2 plays up e. Player 1 plays up; Player 2 plays left f. There is no Nash equilibrium g. Player 1 plays down; Player 2 plays right h. Player 1 plays up; Player 2 plays right i. Player 1 plays left; Player 2 plays up
